UIUC Dept. of Mathematics Seminar Calendar

     August 2011           September 2011          October 2011    
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                                               30 31

Thursday, September 22, 2011

BCDE Math/Physics Seminar
12:00 pm in 464 Loomis Laboratory, Thursday, September 22, 2011

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Submitted by katz.

Charles Rezk (UIUC Math)
K-theory and Reality
Abstract: A "Real" space is a space equipped with an involution. Over such a space, one may define the notion of a "Real" vector bundle, which is a kind of common generalization of the notions of an ordinary vector bundle with respect to either real or complex numbers. I will discuss the resulting "Real" K-theory groups, and their relationship to Clifford modules.

Group Theory Seminar
1:00 pm in Altgeld Hall 347, Thursday, September 22, 2011

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Submitted by kapovich.

Piotr Przytycki (UIUC Math)
Graph manifolds with boundary are virtually special
Abstract: This is joint work with Daniel T. Wise. Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in $\pi_1(M)$, and that the double cosets of crossing surfaces are also separable. We deduce that if there is a "sufficient" collection of embedded surfaces in M, then $\pi_1(M)$ is virtually the fundamental group of a "special" CAT(0) cube complex. That is a complex that admits a local isometry into the Salvetti complex of a right-angled Artin group. We provide a sufficient collection for graph manifolds with boundary thus proving that their fundamental groups are virtually special, in particular linear.

Graduate Geometry and Topology Seminar
2:00 pm in 241 Altgeld Hall, Thursday, September 22, 2011

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Submitted by lukyane2.

Nerses Aramian (UIUC Math)
Unoriented (Co)bordism
Abstract: This talk is going to be a continuation of the talk given last term on cobordism theory. Roughly speaking, in unoriented cobordism one tries to understand when a manifold (without boundary) is a boundary of a higher dimensional manifold. This problem was resolved by R. Thom in his celebrated thesis. Thom used a construction, now called Thom-Pontryagin construction, to translate the problem to one in homotopy theory. In this new setting, the problem can be resolved by the use of various standard techniques in homotopy theory. At the heart of these techniques lies the implementation of stable ordinary cohomology operations (i.e. Steenrod operations).